TSTP Solution File: SET930+1 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n002.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Tue Apr 30 20:40:44 EDT 2024

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   34 (   7 unt;   0 def)
%            Number of atoms       :  105 (  46 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  129 (  58   ~;  37   |;  29   &)
%                                         (   5 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   3 usr;   3 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   61 (  58   !;   3   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = singleton(A)
    <=> ( ~ in(A,C)
        & ( in(B,C)
          | A = B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
    <=> ( ~ in(A,C)
        & ~ in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) = empty_set
    <=> ( in(A,C)
        & in(B,C) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,conjecture,
    ! [A,B,C] :
      ~ ( set_difference(unordered_pair(A,B),C) != empty_set
        & set_difference(unordered_pair(A,B),C) != singleton(A)
        & set_difference(unordered_pair(A,B),C) != singleton(B)
        & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,negated_conjecture,
    ~ ! [A,B,C] :
        ~ ( set_difference(unordered_pair(A,B),C) != empty_set
          & set_difference(unordered_pair(A,B),C) != singleton(A)
          & set_difference(unordered_pair(A,B),C) != singleton(B)
          & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
    inference(negated_conjecture,[status(cth)],[f9]) ).

fof(f13,plain,
    ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f15,plain,
    ! [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) != singleton(A)
        | ( ~ in(A,C)
          & ( in(B,C)
            | A = B ) ) )
      & ( set_difference(unordered_pair(A,B),C) = singleton(A)
        | in(A,C)
        | ( ~ in(B,C)
          & A != B ) ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f16,plain,
    ( ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) != singleton(A)
        | ( ~ in(A,C)
          & ( in(B,C)
            | A = B ) ) )
    & ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = singleton(A)
        | in(A,C)
        | ( ~ in(B,C)
          & A != B ) ) ),
    inference(miniscoping,[status(esa)],[f15]) ).

fof(f19,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X0)
      | in(X0,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f25,plain,
    ! [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
        | ( ~ in(A,C)
          & ~ in(B,C) ) )
      & ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
        | in(A,C)
        | in(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f26,plain,
    ( ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) != unordered_pair(A,B)
        | ( ~ in(A,C)
          & ~ in(B,C) ) )
    & ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = unordered_pair(A,B)
        | in(A,C)
        | in(B,C) ) ),
    inference(miniscoping,[status(esa)],[f25]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = unordered_pair(X0,X1)
      | in(X0,X2)
      | in(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f30,plain,
    ! [A,B,C] :
      ( ( set_difference(unordered_pair(A,B),C) != empty_set
        | ( in(A,C)
          & in(B,C) ) )
      & ( set_difference(unordered_pair(A,B),C) = empty_set
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    inference(NNF_transformation,[status(esa)],[f8]) ).

fof(f31,plain,
    ( ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) != empty_set
        | ( in(A,C)
          & in(B,C) ) )
    & ! [A,B,C] :
        ( set_difference(unordered_pair(A,B),C) = empty_set
        | ~ in(A,C)
        | ~ in(B,C) ) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f34,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = empty_set
      | ~ in(X0,X2)
      | ~ in(X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f35,plain,
    ? [A,B,C] :
      ( set_difference(unordered_pair(A,B),C) != empty_set
      & set_difference(unordered_pair(A,B),C) != singleton(A)
      & set_difference(unordered_pair(A,B),C) != singleton(B)
      & set_difference(unordered_pair(A,B),C) != unordered_pair(A,B) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f36,plain,
    ( set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set
    & set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2)
    & set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_3)
    & set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3) ),
    inference(skolemization,[status(esa)],[f35]) ).

fof(f37,plain,
    set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != empty_set,
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_2),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != singleton(sk0_3),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f40,plain,
    set_difference(unordered_pair(sk0_2,sk0_3),sk0_4) != unordered_pair(sk0_2,sk0_3),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f58,plain,
    ( spl0_0
  <=> in(sk0_2,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f61,plain,
    ( spl0_1
  <=> in(sk0_3,sk0_4) ),
    introduced(split_symbol_definition) ).

fof(f64,plain,
    ( in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4) ),
    inference(resolution,[status(thm)],[f19,f38]) ).

fof(f65,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f64,f58,f61]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( set_difference(unordered_pair(X0,X1),X2) = singleton(X1)
      | in(X1,X2)
      | ~ in(X0,X2) ),
    inference(paramodulation,[status(thm)],[f13,f19]) ).

fof(f76,plain,
    ( ~ in(sk0_2,sk0_4)
    | ~ in(sk0_3,sk0_4) ),
    inference(resolution,[status(thm)],[f34,f37]) ).

fof(f77,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f76,f58,f61]) ).

fof(f80,plain,
    ( in(sk0_3,sk0_4)
    | ~ in(sk0_2,sk0_4) ),
    inference(resolution,[status(thm)],[f66,f39]) ).

fof(f81,plain,
    ( spl0_1
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f80,f61,f58]) ).

fof(f84,plain,
    ( in(sk0_2,sk0_4)
    | in(sk0_3,sk0_4) ),
    inference(resolution,[status(thm)],[f29,f40]) ).

fof(f85,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f84,f58,f61]) ).

fof(f120,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f65,f77,f81,f85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET930+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34  % Computer : n002.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 300
% 0.12/0.34  % DateTime : Mon Apr 29 21:46:24 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.35  % Drodi V3.6.0
% 0.12/0.36  % Refutation found
% 0.12/0.36  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.37  % Elapsed time: 0.020502 seconds
% 0.12/0.37  % CPU time: 0.029516 seconds
% 0.12/0.37  % Total memory used: 12.874 MB
% 0.12/0.37  % Net memory used: 12.805 MB
%------------------------------------------------------------------------------